Determine the maximum bending moment, Mechanical Engineering

Determine the maximum bending moment:

A 12 m span simply supported beam is carrying a consistently distributed load of 2 kN/m over a length of 6 m from the left end and point loads 6 kN, 3 kN and 4 kN at distances of 7 m, 8 m and 9 m, respectively. Draw BM diagram and SF diagram for the beam and determine the maximum bending moment.

2454_Determine the maximum bending moment.png

Figure

Solution

Taking moments around A, and equating to zero.

RB × 12 - (4 × 9) - (3 × 8) - (6 × 7) - 2 × 6 ×(6/2)   = 0

Therefore,        RB = 11.5 kN, and

RA = (2 × 6) + 6 + 3 + 4 - RB = 25 - 11.5 = 13.5 kN

Shear Force (beginning from the left end)

 SF at A, FA = + 13.5 kN

SF at C, FC = + 13.5 - 2 × 6 = + 1.5 kN

SF just left of   D = + 1.5 kN

 SF just right of D = + 1.5 - 6 = - 4.5 kN

SF just left of  E = - 4.5 kN

SF just right of E = - 4.5 - 3 = - 7.5 kN

 SF just left of   F = - 7.5 kN

SF just right of F = - 7.5 - 4 = - 11.5 kN

SF just left of   B = - 11.5 kN = Reaction at B.

Bending Moment

BM at A, MA = 0

BM at C, M  = (13.5 × 6) - 2 × (6 ×(6/2))   = 45 kNm (considering left side)

BM at D, MD = (11.5× 5) - (4 × 2) - (3 × 1) = 46.5 kN m (considering right side)

BM at E,

ME = (11.5 × 4) - (4 × 1) = 42 kN m

BM at F,

MF = (11.5 × 3) = 34.5 kN m

The maximum bending moment take place at D where the shear force changes sign.

                       Mmax = 46.5 kN m.

Posted Date: 1/22/2013 12:44:01 AM | Location : United States







Related Discussions:- Determine the maximum bending moment, Assignment Help, Ask Question on Determine the maximum bending moment, Get Answer, Expert's Help, Determine the maximum bending moment Discussions

Write discussion on Determine the maximum bending moment
Your posts are moderated
Related Questions
Describe the key terms i. Write two differences between boiler and turbine. ii. Compare the rankine cycle with carnot cycle in terms of efficiency and work ratio iii.


Metals and Melting Practices - Alloy,Blowing,Carbon Monoxide Normal 0 false false false EN-IN X-NONE X-NONE Microsoft

Calculate mean effective pressure of engine: A 4 stroke diesel engine is having length of 20 cm and diameter of 16 cm. The engine is generating indicated power of 25 KW when

CLASSIFICATION OF POWER SOURCES ACCORDING TO CONSTRUCTION & DESIGN To give the desired output a power source may be constructed with different components. Therefore, a classifi

estimating time of boring, turning,milling?

With neat diagram illustrate the cycle of operation of four-stroke spark ignition engine. In what respects four-stroke cycle CI engine differ from that of SI engine ?

Calculate quantity of steam in the vessel - thermodynamics: A closed metallic boiler drum having capacity of 0.24m 3 contains steam at pressure of 11bar and a temperature

Limit of proportionality: Limit of proportionality is the stress at which the stress - strain diagram ceases to be a straight line that is, stress at which the extension ceas

Sand Blasting: Historically sand blasting was operated with only using sand only as abrasive media. Today the advance of technologies had brought manufacturer more variety in